A Composite Control Method for a Time-Varying System of Hypersonic Intercept Missiles

Abstract

A composite control method for a time-varying system of a hypersonic interceptor missile, which belongs to the technical field of interceptor missile control. The present invention solves the problem of low execution efficiency of the control system of the time-varying system of the hypersonic interceptor missile caused by only using aerodynamic rudders. In view of the problem that the aerodynamic parameters of the hypersonic interceptor missile change with time during the actual flight process, the present invention applies the LQR and sliding mode methods to the time-varying control system of the interceptor missile. Among them, a controller for the aerodynamic force time-varying system is designed based on the LQR method, and the phase transformation method is used to design a sliding mode controller for the direct lateral force time-varying system, jointly realizing the direct / aerodynamic composite control of the interceptor missile. The method of the present invention can be applied to the control of the time-varying system of the hypersonic interceptor missile.

Description

Technical Field

[0001] The present invention belongs to the technical field of interceptor missile control, and in particular relates to a composite control method for a time-varying system of a hypersonic interceptor missile. Background Art

[0002] Hypersonic interceptors are missiles with flight speeds exceeding 5 Ma, strong penetration capabilities, and significant military and economic value. With the development of modern air defense systems, the demand for near-altitude hypersonic interceptors is increasing, placing particular importance on the design of interceptor control systems. For such missiles, maintaining continuous control force using only aerodynamic rudders is difficult, as this directly leads to inefficient control systems for the interceptor's time-varying system. To achieve better interception effectiveness, a control system that combines direct side force and aerodynamic forces is required.

[0003] Because hypersonic interceptor missiles generate very large normal accelerations during their terminal guidance phase, the aerodynamic parameters of the interceptor control system are time-varying. Due to the complexity of time-varying systems, it is difficult to achieve good performance by designing composite control laws using control methods for non-time-varying systems. Therefore, establishing a time-varying model for the composite system and designing a time-varying control law are particularly necessary. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem of low execution efficiency of the control system of a hypersonic interceptor missile time-varying system caused by using only aerodynamic rudders, and to propose a composite control method for the hypersonic interceptor missile time-varying system.

[0005] The technical solution adopted by the present invention to solve the above technical problems is:

[0006] A composite control method for a time-varying system of a hypersonic interceptor missile, the method specifically comprising the following steps:

[0007] Step 1: Establish a dynamic model of the longitudinal channel of the hypersonic interceptor missile, obtain the state space equation of the longitudinal channel based on the established dynamic model, and design the state feedback control law of the time-varying system aerodynamic rudder based on the state space equation;

[0008] Step 2: Using sliding mode control and phase transformation method, design a sliding mode controller for the longitudinal channel of the time-varying system with direct lateral force;

[0009] Step 3: Use the methods of steps 1 to 2 to design the state feedback control law and sliding mode controller of the yaw channel, and design the controller of the roll channel to achieve control of the time-varying system of the hypersonic interceptor missile.

[0010] Furthermore, the phase conversion method is:

[0011] Consider the linear time-varying system of Equation (11):

[0012]

[0013] where x(t) is the state vector, is the first derivative of x(t), is the input control quantity, and A(t) and B(t) are both time-varying matrices, represents the real number field;

[0014] For the system of Equation (11), the equivalent transformation, that is, the phase transformation formula, is shown in Equation (12):

[0015] z(t) = T(t)x(t) (12)

[0016] where z(t) is the new state variable, T(t) is a non-singular n×n matrix. Differentiating Equation (12) gives:

[0017]

[0018] where, is the first derivative of z(t), is the first derivative of T(t), T(t) -1 is the inverse of T(t), B T = T(t)B(t), A T (t) and B T are written in the form of Equation (14):

[0019]

[0020] where r1(t) ~ r n (t) are the variables after the standard form transformation of the system of Equation (11). Transforming Equation (11) into the standard form of Equation (15):

[0021]

[0022] Furthermore, the specific process of Step 2 is as follows:

[0023] The system model with direct side force is written in the following form:

[0024]

[0025] where the state vector is X1 = [x1 x2 x3 x4] T , is the first derivative of X2, and the control quantity is u2 = F Tyc, F Tyc represents the engine command,

[0026]

[0027] where x1, x2, x3, x4, and x5 are all state variables; a1, a2, a3, a4, and a5 are the aerodynamic parameters of the interceptor, a2 and a4 are time-varying parameters, denoted as a2(t) and a4(t); K(t) is the state feedback controller, K(t)=[K1(t) K2(t) K3(t) K4(t)], and K1(t), K2(t), K3(t), and K4(t) are all elements in K(t); V represents the flight speed of the interceptor, g is the acceleration due to gravity, τ1 represents the dynamic response time constant of the longitudinal channel servo, τ2 represents the dynamic response time constant of the longitudinal channel attitude control engine, k y =1 / (mV), m represents the mass of the interceptor, l z =-l / J z , l represents the distance from the center of force to the center of mass of the interceptor, J z represents the moment of inertia;

[0028] According to equations (11) to (15), using the phase transformation method, that is, using to transform equation (10) into the standard form of equation (16):

[0029]

[0030] where is the state vector of the standard form state equation, is an element in, is the first derivative of, is the transformation matrix, is the inverse of, B3 = [0 0 0 0 1] T ;

[0031] where and are the variables after the standard form transformation of the interceptor time-varying system;

[0032] According to select the switching surface Then the designed sliding mode controller for the longitudinal channel of the time-varying system with direct lateral force is:

[0033]

[0034] Among them, F s is the direct lateral force of the side spray engine. In order to eliminate the chattering phenomenon of the system, a controller with a boundary layer is designed as follows:

[0035]

[0036] Among them, ε > 0;

[0037] Select the amplitude of the control force according to the current flight state and command requirements. When the control force switches between different amplitudes, the expression of variable structure control is:

[0038]

[0039] Among them, F s1 represents the steady thrust of the orbital control engine; F s2 represents the steady thrust of the attitude control engine. ε1 and ε2 are boundary constants and satisfy ε1 > ε2 > 0.

[0040] Furthermore, the method further includes the step of proving the stability of the sliding mode controller of the designed interceptor time-varying system based on the Lyapunov-Krasovskii functional theory. The specific proof process is as follows:

[0041] Assumption 1. Consider that there exist a locally Lipschitz continuous functional V(t), a scalar function μ(t), two κ ∞ functions v i and a κ function γ for the system in Equation (11) that satisfy the following inequality:

[0042]

[0043] Among them, i = 1, 2, is the first derivative of V(t);

[0044] Introduce the scalar function μ(t) and consider the linear time-varying system in Equation (21):

[0045]

[0046] Among them, y(t) is the state of the linear time-varying system in Equation (21), is the first derivative of y(t). If there exist two positive constants k and a such that the solution of Equation (21) satisfies the inequality in Equation (22):

[0047]

[0048] Then, the scalar function μ(t) is uniformly asymptotically stable; e is the base of the natural logarithm;

[0049] If there exist two positive constants \(k_0\) and \(a_0\) such that the solution of Equation (21) satisfies the inequality of Equation (23):

[0050]

[0051] Then, the scalar function \(\mu(t)\) is uniformly exponentially bounded;

[0052] The solution of Equation (21) is:

[0053]

[0054] From Equation (22), the necessary and sufficient condition for the scalar function \(\mu(t)\) to be uniformly asymptotically stable is that there exist two constants \(a \gt 0\) and \(b \geq 0\) satisfying the inequality of Equation (25):

[0055]

[0056] From Equation (23), the necessary and sufficient condition for the scalar function \(\mu(t)\) to be uniformly exponentially bounded is that there exist two constants \(a_0 \gt {0}\) and \(b_0\) satisfying the inequality of Equation (26):

[0057]

[0058] Let \(T\) m be the constant of Equation (27):

[0059]

[0060] Let \(W\) n be defined as:

[0061]

[0062] where \(n\) is a positive constant, \(n \geq 1\), \(V(t)\) satisfies the requirements of Assumption 1, and \(W\) n is a Lyapunov - Krasovskii functional of Equation (11), denoted as:

[0063]

[0064] where, is the first derivative of \(W\) n (t), Let \(\nu\) n \(= a - \frac{nb}{T}\) m \(\gt 0\);

[0065] First, analyze the stability of the system before it is transformed into the standard form, that is, analyze the stability of the system of Equation (10). The specific process is as follows:

[0066] Consider the time-varying system of Equation (10), where the time-varying function is a2(t). After substituting the parameter values of the time-varying system, the two-norm ||B2|| of the function B2 has an upper bound. Consider the Lyapunov function W(X2) = ||X2|| 2 , and the derivative of the Lyapunov function is obtained as follows:

[0067]

[0068] where the scalar function μ(t) is μ(t) = 0.1a2(t), and the matrix D(t) is:

[0069]

[0070] For any time t, the function D(t) is positive definite. According to the scaling method, the derivative of the Lyapunov function W(X2) is further estimated as: Since a2(t) is bounded, for any time t ≥ t0, the scalar function μ is written in the form of Equation (31):

[0071]

[0072] where p and q are constants, and the validity of Equation (25) means that the scalar function μ is uniformly asymptotically stable;

[0073] Similarly, for any time t ≥ t0, the scalar function μ also satisfies:

[0074]

[0075] where p1 and q1 are constants, and the validity of Equation (26) means that the scalar function μ is uniformly exponentially stable;

[0076] Construct the LKF form to prove that the time-varying system of Equation (10) is stable. Let the constant T′ m satisfy:

[0077]

[0078] The LKF expression of the time-varying system of Equation (10) is W n (t) = V(t)φ(t), where the function φ(t) is:

[0079]

[0080] Therefore, the time-varying system of Equation (10) is stable;

[0081] Next, analyze the stability of the system after being transformed into the standard form, that is, the stability of the time-varying system of Equation (16). The specific process is as follows:

[0082] Consider the time-varying system of Equation (16), where the time-varying function is a2(t). After substituting the parameter values of the time-varying system of Equation (16), the two-norm ||B3|| of the function B3 has an upper bound ||B3|| ≤ 1. Consider the Lyapunov function The derivative of the Lyapunov function is obtained as follows:

[0083]

[0084] where the function μ1(t) is The matrix D1(t) is

[0085]

[0086] For any time t, the function D1(t) is positive definite. According to the scaling method, the derivative of the Lyapunov function is further estimated as Since a2(t) is bounded, for any time t ≥ t0, the scalar function μ1 is written in the form of Equation (36):

[0087]

[0088] where p1 and q1 are constants. The establishment of Equation (25) means that the scalar function μ1 is uniformly asymptotically stable;

[0089] Similarly, for any time t ≥ t0, the scalar function μ1 also satisfies

[0090]

[0091] where p1 and q1 are constants. The establishment of Equation (26) means that the scalar function μ1 is uniformly exponentially stable;

[0092] Next, construct the LKF form to prove that the time-varying system of Equation (16) is stable. Let the constant T m1 satisfy

[0093]

[0094] The LKF expression of the time-varying system of Equation (16) is W n (t) = V(t)φ1(t), where the function φ1(t) is

[0095]

[0096] Therefore, the time-varying system of Equation (16) is stable;

[0097] In summary, both the time-varying composite control systems before and after being transformed into the standard form are stable.

[0098] A storage medium stores at least one instruction, and the at least one instruction is loaded and executed by a processor to implement a composite control method for a time-varying system of a hypersonic interceptor.

[0099] The beneficial effects of the present invention are as follows:

[0100] Aiming at the problem that the aerodynamic parameters of a hypersonic interceptor change with time during actual flight, the present invention applies the LQR and sliding mode methods to the time-varying control system of the interceptor. Among them, a controller for the aerodynamic force time-varying system is designed based on the LQR method, and the phase transformation method is used to design a sliding mode controller for the direct lateral force time-varying system, jointly realizing the direct / aerodynamic composite control of the interceptor. It not only compensates for the problem of low control system execution efficiency of the time-varying system of the hypersonic interceptor caused by only using aerodynamic rudders, but also speeds up the rapid response of the interceptor to the tracking of command signals. Moreover, the stability of the designed time-varying control system of the interceptor is proved by applying the Lyapunov-Krasovskii functional (LKF) theory. Description of the Drawings

[0101] Figure 1 is a flowchart of the method of the present invention;

[0102] Figure 2 is a schematic diagram of the tracking response of the interceptor to the overload command in Case 1;

[0103] Figure 3 is a schematic diagram of the change in the angle of attack of the interceptor under the command in Case 1;

[0104] Figure 4 is a schematic diagram of the change in the pitch rate of the interceptor in Case 1;

[0105] Figure 5 is a schematic diagram of the change in the elevator deflection angle of the interceptor in Case 1;

[0106] Figure 6 is a schematic diagram of the change in the engine thrust of the interceptor in Case 1;

[0107] Figure 7 is a schematic diagram of the change in the sliding mode function of the interceptor in Case 1;

[0108] Figure 8 is a schematic diagram of the tracking response of the interceptor to the overload command in Case 2;

[0109] Figure 9 is a schematic diagram of the change in the angle of attack of the interceptor under the command in Case 2;

[0110] Figure 10It is a schematic diagram of the pitch angle rate change of the interceptor missile in Case 2;

[0111] Figure 11 It is a schematic diagram of the elevator deflection angle change of the interceptor missile in Case 2;

[0112] Figure 12 It is a schematic diagram of the engine thrust change of the interceptor missile in Case 2;

[0113] Figure 13 It is a schematic diagram of the sliding mode function change of the interceptor missile in Case 2. Detailed implementation manners

[0114] Detailed implementation manner 1. In combination with Figure 1 This implementation manner will be described. For a composite control method of a hypersonic interceptor missile time-varying system described in this implementation manner, the method specifically includes the following steps:

[0115] Step 1. Establish the dynamic model of the longitudinal channel of the hypersonic interceptor missile, then obtain the state space equation of the longitudinal channel based on the established dynamic model, and design the state feedback control law of the aerodynamic rudder of the time-varying system (applying the LQR (Linear Quadratic Regulator) optimal control method) based on the state space equation;

[0116] Step 2. Use the sliding mode control and phase transformation methods to design the sliding mode controller of the longitudinal channel of the time-varying system with direct lateral force; [[ID=2...]]

[0117] Step 3. Use the methods of Step 1 to Step 2 to design the state feedback control law and the sliding mode controller of the yaw channel, and design the controller of the roll channel to achieve the control of the hypersonic interceptor missile time-varying system. <......]]

[0118] The present invention designs and analyzes the interceptor missile control system in combination with the actual situation, gives the process and method for solving the time-varying controller, and conducts stability analysis, and obtains good results through simulation.

[0119] Detailed implementation manner 2: The difference between this implementation manner and Detailed implementation manner 1 is that the phase transformation method is as follows:

[0120] Consider the linear time-varying system of Equation (11):

[0121]

[0122] where x(t) is the state vector, [[ID=......]] is the first derivative of x(t), is the input control quantity, and A(t) and B(t) are both time-varying matrices, represents the real number field;

[0123] For the system according to Equation (11), the equivalent transformation, that is, the phase transformation formula, is shown in Equation (12):

[0124] z(t) = T(t)x(t) (12)

[0125] where z(t) is the new state variable, and T(t) is a non-singular n×n matrix, which is used to define a new state variable z(t). This transformation can make the system easier to analyze or generalize. Combining Equation (11), differentiating Equation (12) gives:

[0126]

[0127] where is the first derivative of z(t), is the first derivative of T(t), and T(t) -1 is the inverse of T(t), and B T = T(t)B(t), A T (t) and B T are written in the form of Equation (14):

[0128]

[0129] where r1(t) ~ r n (t) are the variables after the standard form transformation of the system in Equation (11). Transforming Equation (11) into the standard form of Equation (15):

[0130]

[0131] Other steps and parameters are the same as those in the specific implementation method one.

[0132] Specific implementation method three: The difference between this implementation method and the first or second specific implementation method is that the state space equation of the longitudinal channel is obtained according to the established dynamic model, and the specific process is as follows:

[0133] For a hypersonic interceptor with near-space compound control, a rudder and a reaction control system are used as actuators to generate aerodynamic force and direct lateral force respectively and act on this missile together. Since the aerodynamic parameters change with time during the flight of the missile, a time-varying model is established for the design and analysis of the missile control system. Here, taking the longitudinal channel as an example, a time-varying compound control law is designed, and the time-varying model (i.e., the dynamic model) of the longitudinal channel is as follows:

[0134]

[0135] where ny is the output overload of the longitudinal channel, is the first derivative of n y , a1, a2, a3, a4 and a5 are the aerodynamic parameters of the interceptor. Here, and a2 and a4 are time-varying parameters, denoted as a2(t) and a4(t); V represents the flight speed of the interceptor, g is the acceleration due to gravity, ω z is the angular velocity, is the first derivative of ω z , τ1 represents the dynamic response time constant of the longitudinal channel servo, τ2 represents the dynamic response time constant of the longitudinal channel attitude control engine, δ z is the rudder deflection angle, is the first derivative of δ z , F Ty represents the engine thrust, is the first derivative of F Ty , δ zc represents the rudder deflection angle command, k y = 1 / (mV), m represents the mass of the interceptor, F Tyc represents the engine command, l z = -l / J z , l represents the distance from the center of force to the center of mass of the interceptor, J z represents the moment of inertia, and respectively represent the partial derivatives of the pitching moment M z with respect to ω z and δ z ; represents the partial derivative of the lift Y with respect to δ z ;

[0136] Define the overload tracking error e y as:

[0137] e y = n yc - n y (2)

[0138] where, n yc represents the overload command. The overload tracking system is expressed as follows:

[0139]

[0140] where, is the first derivative of e y ;

[0141] To improve the tracking accuracy of the overload n y , introduce the tracking error integral term and write Equation (3) in the state space form.

[0142] Define the state variables x1, x2, x3, x4, and x5 as follows: x2 = e y , x3 = ω z , x4 = δ z , x5 = F Ty , where e y is the overload tracking error, ω z is the angular velocity, δ z is the rudder deflection angle, and F Ty represents the engine thrust;

[0143] The control variables u1 and u2 are: u1 = δ zc , u2 = F Tyc , where δ zc represents the rudder deflection command, and F Tyc represents the engine command;

[0144] Then the state - space equation of the longitudinal channel is:

[0145]

[0146] where, is the first - order derivative of x1, is the first - order derivative of x2, is the first - order derivative of x3, is the first - order derivative of x4, is the first - order derivative of x5, V represents the flight speed of the interceptor, g is the acceleration due to gravity, a1, a2, a3, a4, and a5 are the aerodynamic parameters of the interceptor, a2 and a4 are time - varying parameters, denoted as a2(t) and a4(t); and respectively represent the partial derivatives of the pitching moment M z with respect to ω z and δ z , represents the partial derivative of the lift Y with respect to δ z , m represents the mass of the interceptor, J z represents the moment of inertia, k y and l z are both dynamic coefficients, k y = 1 / (mV), l z = -l / J z , l represents the distance from the center of the reaction force to the center of mass of the interceptor, τ1 represents the dynamic response time constant of the longitudinal - channel rudder servo, and τ2 represents the dynamic response time constant of the longitudinal - channel attitude - control engine.

[0147] Other steps and parameters are the same as those in the first or second specific implementation.

[0148] Specific embodiment 4: This embodiment differs from any one of specific embodiments 1 to 3 in that the state feedback control law of the time-varying system aerodynamic rudder is designed based on the state space equation, and the specific process is as follows:

[0149] The design of the composite control law for the control system (4) in step 1 is analyzed in two steps. First, the aerodynamic system controlled by the rudder is analyzed. Then, when the aerodynamic rudder cannot continuously generate control force, the system that adds direct lateral force is analyzed.

[0150] When analyzing the aerodynamic control system, let x5 and u2 be 0, and express the state space equation of formula (4) as:

[0151]

[0152] In the system model of equation (5), the state vector X1 = [x1 x2 x3 x4] T , the control quantity is u1=δ zc , then the state space equation of the system is written as:

[0153]

[0154] in, is the first-order derivative of X1;

[0155]

[0156] Since the rank of the controllability matrices of A1(t) and B1(t) is 4, the system (6) is completely controllable.

[0157] Combining the linear time-varying control theory, the LQR control method is used to design the state feedback control law of the system in equation (6):

[0158] u1=K(t)X1=K1(t)x1+K2(t)x2+K3(t)x3+K4(t)x4 (7)

[0159] Where K(t) is the state feedback controller, K(t) = [K1(t) K2(t) K3(t) K4(t)], K1(t), K2(t), K3(t), K4(t) are all elements in K(t);

[0160] The LQR control method satisfies the following quadratic performance indicators The optimal control law is obtained when :

[0161]

[0162] Among them, t0 is the start time, t fis the end time, both Q(t) and R(t) are diagonal matrices, Q(t) ≥ 0, R(t) > 0, and X1 T (t) is the transpose of X1(t);

[0163] Substitute the control law (7) into the system of equation (6), and the closed-loop system is written as:

[0164]

[0165] where,

[0166]

[0167] Other steps and parameters are the same as those in any one of the specific embodiments one to three.

[0168] Specific embodiment five: The difference between this embodiment and any one of the specific embodiments one to four is that the specific process of step two is as follows:

[0169] For this missile, when the aerodynamic rudder is difficult to continuously generate control force, a direct lateral force needs to be added to the system.

[0170] The system model with the direct lateral force added is written in the following form:

[0171]

[0172] where the state vector is X1 = [x1 x2 x3 x4] T , is the first derivative of X2, the control variable is u2 = F Tyc , F Tyc represents the engine command,

[0173]

[0174] where, x1, x2, x3, x4, and x5 are all state variables; a1, a2, a3, a4, and a5 are the aerodynamic parameters of the interceptor, a2 and a4 are time-varying parameters, denoted as a2(t) and a4(t); K(t) is the state feedback controller, K(t) = [K1(t) K2(t) K3(t) K4(t)], and K1(t), K2(t), K3(t), and K4(t) are all elements in K(t); V represents the flight speed of the interceptor, g is the acceleration due to gravity, τ1 represents the dynamic response time constant of the longitudinal channel servo, τ2 represents the dynamic response time constant of the longitudinal channel attitude control engine, k y = 1 / (mV), m represents the mass of the interceptor, l z = -l / J z, where \(l\) represents the distance from the center of the force to the centroid of the interceptor, and \(J\) z represents the moment of inertia;

[0175] The ranks of the controllability matrices of \(A_2(t)\) and \(B_2\) are 5, that is, the system (10) is completely controllable. Since the direct lateral force controls the system in a switching manner, the sliding mode control method is selected to design the control law.

[0176] According to Eqs. (11) - (15), the phase transformation method is adopted, that is, transform Eq. (10) into the standard form of Eq. (16):

[0177]

[0178] where, is the state vector of the standard form state equation, is an element in, [[ID=2,5]] is the first derivative of, is the transformation matrix, is the inverse of, B3 = [0 0 0 0 1] T ;

[0179] where, and are the variables after the standard form transformation of the interceptor time-varying system; after substituting the various parameters of the system, the result of \(A_3(t)\) can be obtained, which provides convenience for the next stability analysis of the system. Here, \(a_4(t)\) has a certain proportional relationship with \(a_2(t)\), and \(a_4(t)\) is expressed in the form of \(a_2(t)\), denoted as \(a_4(t)=k\) a * \(a_2(t)\), where \(k\) a = -0.042. The matrix of \(A_3(t)\) after transformation into the standard form is:

[0180]

[0181] that is

[0182] where, represents and the others are the same;

[0183] According to select the switching surface Then the sliding mode controller of the longitudinal channel of the time-varying system with direct lateral force designed is:

[0184]

[0185] Among them, F s is the direct lateral force of the side jet engine. Since the system of Equation (10) can be transformed into the standard form of Equation (16), the points on the sliding surface can converge to zero. To eliminate the chattering phenomenon of the system, a controller with a boundary layer is designed as follows:

[0186]

[0187] Among them, ε > 0, and ε represents a small positive value;

[0188] The engines of the control system include orbit control engines and attitude control engines. Different engines output different magnitudes of reaction forces and reaction torques. The magnitude of the control force suitable for the current system can be selected according to the current flight state and command requirements. The control force switches between different magnitudes. If the current state of the system is far from the sliding surface, a larger thrust is obtained, while if the current state of the system is close to the sliding surface, a smaller thrust is obtained. Then the expression of variable structure control is:

[0189]

[0190] Among them, F s1 represents the steady-state thrust of the orbit control engine; F s2 represents the steady-state thrust of the attitude control engine. ε1 and ε2 are boundary constants and satisfy ε1 > ε2 > 0.

[0191] Equations (11) to (15) are equivalent to a basis for phase transformation. Based on the theory of Equations (11) to (15), Equation (10) is transformed into the standard form of Equation (16). The phase transformation method is an equivalent transformation between time-varying systems, used to simplify a system or transform it into a certain ideal standard form. In this invention, solving the sliding mode control law based on the phase transformation method is to simplify the system during the time-varying sliding mode control process, making the control process simpler and the control effect better. Transforming the original system into a standard form system is convenient for analysis, and the theoretical basis for calculation is stronger.

[0192] Other steps and parameters are the same as those in any one of the first to fourth specific embodiments.

[0193] Specific Embodiment Six: The difference between this embodiment and any one of the first to fifth specific embodiments is that the method further includes the step of proving the stability of the sliding mode controller of the designed interceptor time-varying system based on the Lyapunov-Krasovskii functional (LKF) theory. The specific proof process is as follows:

[0194] First, review a hypothesis, which is the premise for constructing the Lyapunov-Krasovskii functional.

[0195] Hypothesis 1. Consider that there exist a locally Lipschitz continuous functional V(t), a scalar function μ(t), two κ ∞ functions v i and a κ function γ for the system in Equation (11), satisfying the following inequalities:

[0196]

[0197] where i = 1, 2, is the first derivative of V(t);

[0198] Introduce the concept of the scalar function μ(t) and consider the linear time-varying system in Equation (21):

[0199]

[0200] where y(t) is the state of the linear time-varying system in Equation (21), is the first derivative of y(t). If there exist two positive constants k and a such that the solution of the scalar system in Equation (21) satisfies the inequality in Equation (22):

[0201]

[0202] then the scalar function μ(t) is uniformly asymptotically stable; e is the base of the natural logarithm;

[0203] If there exist two positive constants k0 and a0 such that the solution of the scalar system in Equation (21) satisfies the inequality in Equation (23):

[0204]

[0205] then the scalar function μ(t) is uniformly exponentially bounded;

[0206] The solution of Equation (21) is:

[0207]

[0208] From Equation (22), the necessary and sufficient condition for the scalar function μ(t) to be uniformly asymptotically stable is that there exist two constants a > 0 and b ≥ 0 satisfying the inequality in Equation (25):

[0209]

[0210] From Equation (23), the necessary and sufficient condition for the scalar function μ(t) to be uniformly exponentially bounded is that there exist two constants a0 > 0 and b0 satisfying the inequality in Equation (26):

[0211]

[0212] Finally, a Lyapunov-Krasovskii functional is constructed to analyze the stability of time-varying systems. Considering the system (11) under the premise of Assumption 1, the scalar function μ(t) needs to satisfy equations (25) and (26) to be uniformly asymptotically stable and uniformly exponentially bounded;

[0213] Let T m be the constant in equation (27):

[0214]

[0215] W n is defined as:

[0216]

[0217] where denotes the right-hand side of the formula for defining W n (t), n is a positive constant, n ≥ 1, V(t) satisfies the requirements of Assumption 1, and W n is a Lyapunov-Krasovskii functional (LKF) of equation (11), denoted as:

[0218]

[0219] where is the first derivative of W n (t), ν n = a - nb / T m > 0;

[0220] According to the above theory and steps, analyze the stability of the designed system. First, analyze the stability of the system before conversion to the standard form, and then analyze the stability of the system after conversion to the standard form. If the systems before and after conversion are both stable, then the designed system is stable, and it is shown that the transformation process has no effect on the system stability.

[0221] First, analyze the stability of the system before conversion to the standard form, that is, analyze the stability of the system of equation (10). The specific process is as follows:

[0222] Consider the time-varying system of equation (10), where the time-varying function is a2(t). After substituting the parameter values of the time-varying system, the two-norm ||B2|| of the function B2 has an upper bound, ||B2|| ≤ 1001. Consider the Lyapunov function W(X2) = ||X2|| 2 , and the derivative of Lyapunov is obtained as:

[0223]

[0224] where the scalar function μ(t) is μ(t) = 0.1a2(t), and the matrix D(t) is:

[0225]

[0226] For any time t, the function D(t) is positive definite. According to the scaling method, the derivative of the Lyapunov function W(X2) is further estimated as: Since a2(t) is bounded, for any time t ≥ t0, the scalar function μ is written in the form of Equation (31):

[0227]

[0228] where p and q are constants. The establishment of Equation (25) means that the scalar function μ is uniformly asymptotically stable;

[0229] Similarly, for any time t ≥ t0, the scalar function μ also satisfies:

[0230]

[0231] where p1 and q1 are constants. The establishment of Equation (26) means that the scalar function μ is uniformly exponentially stable;

[0232] Next, construct the LKF form to prove that the time-varying system of Equation (10) is stable. Let the constant T′ m satisfy:

[0233]

[0234] The LKF of the time-varying system of Equation (10) can be expressed as W n (t) = V(t)φ(t), where the function φ(t) is:

[0235]

[0236] Therefore, the time-varying system of Equation (10) is stable;

[0237] Next, analyze the stability of the system after being transformed into the standard form, that is, the stability of the time-varying system of Equation (16). The specific process is as follows:

[0238] Consider the time-varying system of Equation (16), where the time-varying function is a2(t). After substituting the parameter values of the time-varying system of Equation (16), the two-norm ||B3|| of the function B3 has an upper bound ||B3|| ≤ 1. Consider the Lyapunov function The derivative of Lyapunov is obtained as:

[0239]

[0240] Among them, the function μ1(t) is The matrix D1(t) is:

[0241]

[0242] For any time t, the function D1(t) is positive definite. According to the scaling method, the derivative of the Lyapunov function is further estimated as: Since a2(t) is bounded, for any time t≥t0, the scalar function μ1 is written in the form of Equation (36):

[0243]

[0244] where p1 and q1 are constants. When Equation (25) holds, the scalar function μ1 is uniformly asymptotically stable;

[0245] Similarly, for any time t≥t0, the scalar function μ1 also satisfies:

[0246]

[0247] where p1 and q1 are constants. When Equation (26) holds, the scalar function μ1 is uniformly exponentially stable;

[0248] Next, construct the LKF form to prove that the time-varying system of Equation (16) is stable. Let the constant T m1 satisfy:

[0249]

[0250] The LKF expression of the time-varying system of Equation (16) is W n (t) = V(t)φ1(t), where the function φ1(t) is:

[0251]

[0252] Therefore, the time-varying system of Equation (16) is stable;

[0253] In summary, the time-varying composite control systems before and after being transformed into the standard form are both stable.

[0254] Other steps and parameters are the same as those in any one of the specific embodiments one to five.

[0255] Specific Embodiment Seven: This embodiment is a storage medium, in which at least one instruction is stored, and the at least one instruction is loaded and executed by a processor to implement the composite control method of the hypersonic interceptor time-varying system.

[0256] It should be understood that any method described in the present invention can be provided as a computer program product, software, or a computerized method, which may include a non-transitory machine-readable medium storing instructions thereon, and the instructions can be used to program a computer system or other electronic devices. The storage medium may include, but is not limited to, magnetic storage media, optical storage media; magneto-optical storage media include: read-only memory ROM, random access memory RAM, erasable programmable memory (e.g., EPROM and EEPROM), and flash memory layers; or other types of media suitable for storing electronic instructions.

[0257] Emulation part

[0258] The present invention emulates the hypersonic near-space interceptor missile at a flight altitude of 30 km, and emulates the time-varying composite control system of the longitudinal channel in two cases. Case 1: Tracking the step signal n yc = 10, and the simulation results are as shown in Figures 2 to 7 ; Case 2: Tracking the step plus sine signal n yc = 7 + 3sin(2πt / 2), and the simulation results are as shown in Figures 8 to 13 . The relevant simulation parameters of the interceptor missile are shown in Table 1:

[0259] Table 1

[0260]

[0261] Figure 2 Among them, the simulation results show that the rise time of the overload command for the straight / gas composite time-varying control system of the interceptor missile to track the step signal is 0.22 s, and the overshoot is very small. Figure 3 In, the angle-of-attack response and the overload response of the control system are synchronized, and the steady-state process remains stable. Figure 4 In, the maximum value of the pitch angle rate is 158 / s, and it stabilizes near the zero axis after the angle of attack is established. Figure 5 During the dynamic process of, the elevator deflection angle of the straight / gas composite control system is saturated to a certain extent, the steady state is stable, the system state is stabilized on the sliding mode surface, and converges to the origin. Figure 6 In, the attitude and trajectory control engine works during the dynamic process, shuts down in the steady state, and maintains a stable state. Figure 7 In, the sliding mode function of the straight / gas composite control system quickly converges to the sliding mode surface and remains stable at 0.22 s. According to the simulation analysis, the feasibility of the designed control method for the interceptor missile is verified.

[0262] Similarly, Figure 8 Among them, the simulation results show that the rise time of the overload command for the straight / gas composite time-varying control system of the interceptor missile to track the step and sine composite signal is 0.5 s, and the overshoot is very small. Figure 9 In, the angle-of-attack response and the overload response of the control system are synchronized, and the steady-state process remains stable.Figure 10 The maximum value of the pitch angle rate is 120.2 / s, and it stabilizes near the zero axis and varies sinusoidally after the angle of attack is established. Figure 11 During the dynamic process of, the elevator deflection angle of the direct / gas composite control system is saturated to a certain extent, and the steady state is stable. Figure 12 In, the attitude and orbit control engine operates during the dynamic process, shuts down in the steady state, and maintains a stable state. Figure 13 In, the sliding mode function of the direct / gas composite control system quickly converges to the sliding mode surface and remains stable at 0.4 s. According to the simulation analysis, the feasibility of the designed interceptor control method is verified.

[0263] Based on the simulation analysis of the above two cases, the feasibility of the designed interceptor control method is verified.

[0264] The above examples of the present invention are only for explaining in detail the calculation model and calculation process of the present invention, and are not intended to limit the implementation manner of the present invention. For those of ordinary skill in the art, other different forms of changes or variations can be made based on the above description. It is impossible to list all the implementation manners here. Any obvious changes or variations derived from the technical solution of the present invention still fall within the protection scope of the present invention.

Claims

1. A composite control method for a time-varying system of a hypersonic interceptor missile, characterized in that: The method specifically comprises the following steps: Step 1: Establish a dynamic model of the longitudinal channel of the hypersonic interceptor missile, obtain the state space equation of the longitudinal channel based on the established dynamic model, and design the state feedback control law of the time-varying system aerodynamic rudder based on the state space equation; Step 2: Using sliding mode control and phase transformation method, design a sliding mode controller for the longitudinal channel of the time-varying system with direct lateral force; The phase conversion method is: Consider the linear time-varying system of formula (11): Where x(t) is the state vector, is the first derivative of x(t), is the input control quantity, A(t) and B(t) are both time-varying matrices, represents the field of real numbers; According to the system of formula (11), the equivalent transformation, that is, the phase transformation formula is shown in formula (12): z(t)=T(t)x(t) (12) Where z(t) is the new state variable and T(t) is a non-singular n×n matrix. Derivative (12) yields: in, is the first derivative of z(t), is the first-order derivative of T(t), T(t) -1 is the inverse of T(t), B T =T(t)B(t), A T (t) and B T The form of writing formula (14) is: Among them, r1(t)~r n (t) is the variable after the system standard form conversion of formula (11), which converts formula (11) into the standard form of formula (15): Step 3: Use the methods of steps 1 to 2 to design the state feedback control law and sliding mode controller of the yaw channel, and design the controller of the roll channel to achieve control of the time-varying system of the hypersonic interceptor missile.

2. The composite control method for a time-varying system of a hypersonic interceptor missile according to claim 1, characterized in that: The specific process of step 2 is: The system model with direct lateral force is written as follows: The state vector is X1=[x1x2 x3 x4] T , is the first-order derivative of X2, and the control quantity is u2=F Tyc , F Tyc Indicates engine command, Among them, x1, x2, x3, x4 and x5 are all state variables; a2, a4 and a5 are the aerodynamic parameters of the interceptor missile, a2 and a4 are time-varying parameters, denoted as a2(t) and a4(t); K(t) is the state feedback controller, K(t) = [K1(t)K2(t)K3(t)K4(t)], K1(t), K2(t), K3(t), K4(t) are all elements in K(t); V represents the flight speed of the interceptor missile, g is the acceleration of gravity, τ1 represents the dynamic response time constant of the longitudinal channel servo, τ2 represents the dynamic response time constant of the longitudinal channel attitude control engine, k y =1 / (mV), m represents the mass of the interceptor missile, l z =-l / J z , l is the distance from the center of force to the center of mass of the interceptor missile, J z represents the moment of inertia; According to formula (11) to formula (15), the phase transformation method is adopted, that is, Convert Equation (10) into the standard form of Equation (16): in, is the state vector of the standard state equation, for The elements in yes The first derivative of is the transformation matrix, yes The inverse, B3=[00001] T ; in, and It is the variable after the standard type conversion of the interceptor missile time-varying system; according to Select Switching Side The designed sliding mode controller for the longitudinal channel of the time-varying system with direct lateral force is: Among them, F s is the direct lateral force of the side jet engine. In order to eliminate the buffeting phenomenon of the system, a controller with a boundary layer is designed as follows: Among them, ε>0; The amplitude of the control force is selected according to the current flight state and command requirements, and the control force switches between different amplitudes. The expression of variable structure control is: Among them, F s1 represents the steady-state thrust of the orbital control engine; F s2 represents the steady-state thrust of the attitude control engine, ε1 and ε2 are boundary constants, and satisfy ε1>ε2>0.

3. The composite control method for a time-varying system of a hypersonic interceptor missile according to claim 2, characterized in that: The method further includes a step of proving the stability of the sliding mode controller of the designed interceptor missile time-varying system based on the Lyapunov-Krasovskii functional theory. The specific proof process is as follows: Assumption 1. Consider the system of Equation (11) where there exists a local Lipschitz continuous functional V(t), a scalar function μ(t), two κ ∞ Function v i and a kappa function γ that satisfies the following inequality: Where i = 1, 2, is the first derivative of V(t); Introducing the scalar function μ(t), consider the linear time-varying system of Equation (21): Where y(t) is the state of the linear time-varying system of Equation (21), is the first-order derivative of y(t). If there exist two positive constants k and a such that the solution of Equation (21) satisfies the inequality of Equation (22): Then, the scalar function μ(t) is uniformly asymptotically stable; e is the base of the natural logarithm; If there exist two positive constants k0 and a0 such that the solution of equation (21) satisfies the inequality of equation (23): Then, the scalar function μ(t) is uniformly exponentially bounded; The solution of formula (21) is: From Equation (22), we know that the necessary and sufficient condition for the scalar function μ(t) to be uniformly asymptotically stable is that there exist two constants a>0 and b≥0 that satisfy the inequality of Equation (25): From Equation (23), we know that the necessary and sufficient condition for the scalar function μ(t) to be uniformly exponentially bounded is that there exist two constants a0>0 and b0 that satisfy the inequality of Equation (26): Assume T m is the constant of formula (27): W n is defined as: Where n is a positive constant, n≥1, V(t) satisfies the requirements of Assumption 1, W n is a Lyapunov-Krasovskii functional of formula (11), denoted as: in, It's W n The first derivative of (t), ν n =a-nb / T m >0; First, we analyze the stability of the system before converting to the standard form, that is, the stability of the system of formula (10). The specific process is as follows: Consider the time-varying system of formula (10), where the time-varying function is a2(t). After substituting the parameter values of the time-varying system, the second norm of the function B2 ||B2|| has an upper bound. Consider the Lyapunov function W(X2) = ||X2|| 2 , and the Lyapunov derivative is: Where the scalar function μ(t) is μ(t)=0.1a2(t), and the matrix D(t) is: For any time t, the function D(t) is positive definite. According to the scaling method, the derivative of the Lyapunov function W(X2) is further estimated as: Since a2(t) is bounded, for any time t≥t0, the scalar function μ is written in the form of formula (31): Where p and q are constants, and Equation (25) becomes the scalar function μ, which is uniformly asymptotically stable. Similarly, for any time t≥t0, the scalar function μ also satisfies: Where p1,q1 are constants, and Equation (26) forms the scalar function μ, which is uniformly exponentially stable; Construct LKF formalism to prove that the time-varying system of Equation (10) is stable. Let the constant T m 'satisfy: The LKF expression of the time-varying system of formula (10) is W n (t) = V(t)φ(t), where the function φ(t) is: Therefore, the time-varying system of formula (10) is stable; Next, we analyze the stability of the system after conversion to the standard form, that is, the stability of the time-varying system of formula (16). The specific process is as follows: Consider the time-varying system of formula (16), the time-varying function is a2(t), after substituting the parameter values of the time-varying system of formula (16), the second norm of the function B3 ||B3|| has an upper bound ||B3||≤1, considering the Lyapunov function The Lyapunov derivative is obtained as: Among them, the function μ1(t) is The matrix D1(t) is: For any time t, the function D1(t) is positive definite. According to the scaling method, the Lyapunov function The derivative of is further estimated as: Since a2(t) is bounded, for any time t≥t0, the scalar function μ1 is written in the form of formula (36): Where p1,q1 are constants, and Equation (25) becomes the scalar function μ1, which is uniformly asymptotically stable; Similarly, for any time t≥t0, the scalar function μ1 also satisfies: Where p1,q1 are constants, and Equation (26) becomes the scalar function μ1, which is uniformly exponentially stable; Next, we construct the LKF form to prove that the time-varying system of Equation (16) is stable. Let the constant T m1 satisfy: The LKF expression of the time-varying system of formula (16) is W n (t)=V(t)φ1(t), where the function φ1(t) is: Therefore, the time-varying system of Equation (16) is stable; Based on the above analysis, the time-varying composite control system is stable before and after being converted into the standard type.

4. A storage medium, characterized in that The storage medium stores at least one instruction, and the at least one instruction is loaded and executed by the processor to implement the composite control method of the time-varying system of a hypersonic interceptor missile as described in any one of claims 1 to 3.

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